A267958 4 times A042965.

0, 4, 12, 16, 20, 28, 32, 36, 44, 48, 52, 60, 64, 68, 76, 80, 84, 92, 96, 100, 108, 112, 116, 124, 128, 132, 140, 144, 148, 156, 160, 164, 172, 176, 180, 188, 192, 196, 204, 208, 212, 220, 224, 228, 236, 240, 244, 252, 256, 260, 268, 272, 276, 284, 288, 292, 300, 304

Offset

1,2

Comments

Ordered list of differences between even squares.

Links

Table of n, a(n) for n=1..58.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

Numbers of the form (2m)^2 - (2n)^2, sorted.

From Chai Wah Wu, Sep 01 2024: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n > 4.

G.f.: 4*x^2*(x + 1)^2/(x^4 - x^3 - x + 1). (End)

Example

(2*0)^2 - (2*0)^2 = 0,
(2*1)^2 - (2*0)^2 = 4,
(2*2)^2 - (2*1)^2 = 12,
(2*2)^2 - (2*0)^2 = 16,
(2*3)^2 - (2*2)^2 = 20,
...

Maple

a := proc(n) option remember; if n = 1 then 0 elif n = 2 then 4 elif n = 3 then 12 else a(floor((1/2)*n)) + a(1+ceil((1/2)*n)) end if; end proc:
seq(a(n), n = 1..50); # Peter Bala, Aug 03 2022

Prog

(Python)
def DifferenceOfEvenSquares(maximumBound):
    sequence = set([0])
    for x in range(0, maximumBound+1, 4):
        if x % 16 != 8:
            sequence.add(x)
    print(sorted(sequence))

Crossrefs

Cf. A008590, A042965.

Sequence in context: A342090 A365889 A310565 * A077770 A310566 A108269

Adjacent sequences: A267955 A267956 A267957 * A267959 A267960 A267961

Keyword

easy,nonn

Author

Matthew Burch, Jan 22 2016

Status

approved